statsmodels.tsa.statespace.representation.Representation¶
- class statsmodels.tsa.statespace.representation.Representation(k_endog, k_states, k_posdef=None, initial_variance=1000000.0, nobs=0, dtype=<class 'numpy.float64'>, design=None, obs_intercept=None, obs_cov=None, transition=None, state_intercept=None, selection=None, state_cov=None, statespace_classes=None, **kwargs)[source]¶
State space representation of a time series process
- Parameters:¶
- k_endog{array_like,
int} The observed time-series process \(y\) if array like or the number of variables in the process if an integer.
- k_states
int The dimension of the unobserved state process.
- k_posdef
int,optional The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. Must be less than or equal to k_states. Default is k_states.
- initial_variance
float,optional Initial variance used when approximate diffuse initialization is specified. Default is 1e6.
- initialization
Initializationobjectorstr,optional Initialization method for the initial state. If a string, must be one of {‘diffuse’, ‘approximate_diffuse’, ‘stationary’, ‘known’}.
- initial_statearray_like,
optional If initialization=’known’ is used, the mean of the initial state’s distribution.
- initial_state_covarray_like,
optional If initialization=’known’ is used, the covariance matrix of the initial state’s distribution.
- nobs
int,optional If an endogenous vector is not given (i.e. k_endog is an integer), the number of observations can optionally be specified. If not specified, they will be set to zero until data is bound to the model.
- dtype
np.dtype,optional If an endogenous vector is not given (i.e. k_endog is an integer), the default datatype of the state space matrices can optionally be specified. Default is np.float64.
- designarray_like,
optional The design matrix, \(Z\). Default is set to zeros.
- obs_interceptarray_like,
optional The intercept for the observation equation, \(d\). Default is set to zeros.
- obs_covarray_like,
optional The covariance matrix for the observation equation \(H\). Default is set to zeros.
- transitionarray_like,
optional The transition matrix, \(T\). Default is set to zeros.
- state_interceptarray_like,
optional The intercept for the transition equation, \(c\). Default is set to zeros.
- selectionarray_like,
optional The selection matrix, \(R\). Default is set to zeros.
- state_covarray_like,
optional The covariance matrix for the state equation \(Q\). Default is set to zeros.
- **kwargs
Additional keyword arguments. Not used directly. It is present to improve compatibility with subclasses, so that they can use **kwargs to specify any default state space matrices (e.g. design) without having to clean out any other keyword arguments they might have been passed.
- k_endog{array_like,
- Attributes:¶
- nobs
int The number of observations.
- k_endog
int The dimension of the observation series.
- k_states
int The dimension of the unobserved state process.
- k_posdef
int The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation.
- shapes
dictionaryofname:tuple A dictionary recording the initial shapes of each of the representation matrices as tuples.
- initialization
str Kalman filter initialization method. Default is unset.
- initial_variance
float Initial variance for approximate diffuse initialization. Default is 1e6.
- nobs
Notes
A general state space model is of the form
\[\begin{split}y_t & = Z_t \alpha_t + d_t + \varepsilon_t \\ \alpha_t & = T_t \alpha_{t-1} + c_t + R_t \eta_t \\\end{split}\]where \(y_t\) refers to the observation vector at time \(t\), \(\alpha_t\) refers to the (unobserved) state vector at time \(t\), and where the irregular components are defined as
\[\begin{split}\varepsilon_t \sim N(0, H_t) \\ \eta_t \sim N(0, Q_t) \\\end{split}\]The remaining variables (\(Z_t, d_t, H_t, T_t, c_t, R_t, Q_t\)) in the equations are matrices describing the process. Their variable names and dimensions are as follows
Z : design \((k\_endog \times k\_states \times nobs)\)
d : obs_intercept \((k\_endog \times nobs)\)
H : obs_cov \((k\_endog \times k\_endog \times nobs)\)
T : transition \((k\_states \times k\_states \times nobs)\)
c : state_intercept \((k\_states \times nobs)\)
R : selection \((k\_states \times k\_posdef \times nobs)\)
Q : state_cov \((k\_posdef \times k\_posdef \times nobs)\)
In the case that one of the matrices is time-invariant (so that, for example, \(Z_t = Z_{t+1} ~ \forall ~ t\)), its last dimension may be of size \(1\) rather than size nobs.
References
Methods
bind(endog)Bind data to the statespace representation
clone(endog, **kwargs)Clone a state space representation while overriding some elements
diff_endog(new_endog[, tolerance])extend(endog[, start, end])Extend the current state space model, or a specific (time) subset
initialize(initialization[, ...])Create an Initialization object if necessary
initialize_approximate_diffuse([variance])Initialize the statespace model with approximate diffuse values.
initialize_components([a, Pstar, Pinf, A, ...])Initialize the statespace model with component matrices
Initialize the statespace model as diffuse.
initialize_known(constant, stationary_cov)Initialize the statespace model with known distribution for initial state.
Initialize the statespace model as stationary.
Properties
(array) Design matrix: \(Z~(k\_endog \times k\_states \times nobs)\)
(dtype) Datatype of currently active representation matrices
(array) The observation vector, alias for obs.
(array) Observation vector: \(y~(k\_endog \times nobs)\)
(array) Observation covariance matrix: \(H~(k\_endog \times k\_endog \times nobs)\)
(array) Observation intercept: \(d~(k\_endog \times nobs)\)
(str) BLAS prefix of currently active representation matrices
(array) Selection matrix: \(R~(k\_states \times k\_posdef \times nobs)\)
(array) State covariance matrix: \(Q~(k\_posdef \times k\_posdef \times nobs)\)
(array) State intercept: \(c~(k\_states \times nobs)\)
(bool) Whether or not currently active representation matrices are time-invariant
(array) Transition matrix: \(T~(k\_states \times k\_states \times nobs)\)